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An analytically based method is proposed to simulate the acoustic-gravity waves in the horizontally stratified atmosphere-Earth structure generated by a point force on the Earth's surface. The method solves the linear momentum, continuity and adiabaticity equations in the atmosphere and elastodynamic equations in the solid Earth in the frequency–wavenumber domain. The time-domain waveforms are obtained by wavenumber integration and fast Fourier transform with respect to the frequency. Numerical simulations are conducted to investigate the properties of the acoustic-gravity waves, including both the high-frequency acoustic-mode waves and low-frequency gravity-mode waves. Simulations of the high-frequency responses show that disturbances in the atmosphere with three apparent horizontal velocities can be identified. They are, namely, the direct acoustic-mode wave generated by source travelling with the sound speed, the head wave generated by the seismic P -wave travelling with apparent horizontal speed identical to the P velocity, and the head wave generated by the Rayleigh wave with a horizontal speed same to the Rayleigh wave velocity. Simulations of the low-frequency responses show that the gravity-mode wave and Lamb wave can be identified. The gravity-mode wave travels with a speed lower than the sound seed and does not reach everywhere, especially the area directly above the source. The Lamb wave travels along the Earth surface with a speed of about 310 m s–1 and its energy decays with the altitude. We also apply our method to explaining the Doppler sounding data observed in Taiwan area during the 2011 Tohoku M 9 earthquake, and find good agreement between the predicted signals and observed data in the arrival time and wave envelope associated with the Rayleigh wave. [ABSTRACT FROM AUTHOR]